Current methods for determining the mathematical derivative of first, second and higher order polynomial functions typically involve purely mathematical problem solving techniques. Such prior art methods typically require that the exponent of the variable be multiplied times the coefficient of the same factor of the polynomial, and that the variable exponent be decreased by one. An example of prior art mathematical differential methods can be illustrated by the following equation: EQU f(x)=4x.sup.2 +2x+1
with the derivative being: EQU d(f(x))/dx[=4(2)x.sup.2-1 +2x.sup.1-1 EQU d(f(x))/dx=8x+2
Such purely mathematical methods for performing differentiation are well recognized and widely practiced. They are, however, limited in that a person initially learning to mathematically differentiate typically cannot see the relationship between such operations and the underlying concepts of the polynomial expression and the purpose for such operations. Such purely mathematical methods for differentiation also fail to provide a method for differentiating which involves manipulation of structural elements. Nor do such prior art techniques provide methods employing structural elements which are highly illustrative of mathematical relationships, tactile in nature, and extremely helpful in both structurally solving the problems and in illustrating the process being performed.